A fluctuation theorem for non-equilibrium relaxational systems driven by external forces

Zamponi, Francesco; Bonetto, Federico; Cugliandolo, Leticia F.; Kurchan, Jorge

doi:10.1088/1742-5468/2005/09/p09013

Cited by 121 publications

(183 citation statements)

References 64 publications

(197 reference statements)

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“…However, it might also be interesting to experimentally check for anomalous work TFR in case of a particle dragged through a highly viscous gel instead of through water [27], for the fluctuations of a driven pendulum in gel [101], for granular gases exhibiting subdiffusion [102], or for glassy systems [54,61,69]. On the theoretical side, the basic results reported in this chapter suggest to systematically check the remaining variety of conventional fluctuation relations [9,10,11] for anomalous generalizations.…”

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confidence: 89%

“…Probably inspired by the experiment of Ref. [27], typically Langevin dynamics in a harmonic potential moving with a constant velocity has been studied in the literature [48,49,50,61], cf. Fig.…”

Section: Transient Fluctuation Relation For Ordinary Langevin Dynamicsmentioning

confidence: 99%

“…We remark that for driven glassy systems FRs have already been obtained displaying slopes that are not equal to one. Within this context it has been suggested to capture these deviations from one by introducing the concept of an 'effective temperature' [61,68,69]. As far as the time dependence of the coefficient is concerned, such behavior has recently been observed in computer simulations of a paradigmatic two dimensional lattice gas model generating glassy dynamics [54].…”

Section: Correlated External Gaussian Noisementioning

confidence: 99%

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Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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Abstract. We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: Lévy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.

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mentioning

confidence: 89%

Section: Transient Fluctuation Relation For Ordinary Langevin Dynamicsmentioning

confidence: 99%

Section: Correlated External Gaussian Noisementioning

confidence: 99%

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Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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“…In fact the very definition of the duality between currents and fluxes so familiar in nonequilibrium thermodynamics since Onsager can be set up in such systems using as generating function the σ + regarded as a function of E. Note that the fluxes are usually "currents" divided by the temperature: therefore via the above interpretation one can try to define the temperature even in nonequilibrium situations, [8,19,20].…”

Section: Conservative Systems and The Equilibrium Limitmentioning

confidence: 99%

Chaotic Hypothesis, Fluctuation Theorem and Singularities

et al. 2006

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The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention and can lead to apparent inconsistencies. In particular there are several cases that have been considered in the literature in which singularities are built in the models: for instance when among the forces there are Lennard-Jones potentials (which are infinite in the origin) and the constraints imposed on the system do not forbid arbitrarily close approach to the singularity even though the average kinetic energy is bounded. The situation is well understood in certain special cases in which the system is subject to Gaussian noise; here the treatment of rather general singular systems is considered and the predictions of the chaotic hypothesis for such situations are derived. The main conclusion is that the chaotic hypothesis is perfectly adequate to describe the singular physical systems we consider, i.e. deterministic systems with thermostat forces acting according to Gauss' principle for the constraint of constant total kinetic energy ("isokinetic Gaussian thermostats"), close and far from equilibrium. Near equilibrium it even predicts a fluctuation relation which, in deterministic cases with more general thermostat forces (i.e. not necessarily of Gaussian isokinetic nature), extends recent relations obtained in situations in which the thermostatting forces satisfy Gauss' principle. This relation agrees, where expected, with the fluctuation theorem for perfectly chaotic systems. The results are compared with some recent works in the literature.

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“…A major "test bed" for fluctuation theorems is provided by dynamical systems with a few degrees of freedom coupled to a thermal bath, a Brownian particle being an example. Much of the corresponding theoretical and experimental work refers to (i) modulated linear systems, where fluctuations have been studied both in transient and stationary regimes [6,7,8,9,10,11,12], and (ii) nonlinear systems, initially at thermal equilibrium, driven to a different, generally nonequilibrium state [13,14,15,16,17].…”

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confidence: 99%

Exponential peak and scaling of work fluctuations in modulated systems

Dykman

2008

Phys. Rev. E

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We extend the stationary-state work fluctuation theorem to periodically modulated nonlinear systems. Such systems often have coexisting stable periodic states. We show that work fluctuations sharply increase near a kinetic phase transition where the state populations are close to each other. The work variance is proportional here to the reciprocal rate of interstate switching. We also show that the variance displays scaling with the distance to a bifurcation point and find the critical exponent for a saddle-node bifurcation.PACS numbers: 05.70.Ln, 74.50.+r, 85.85.+j Since their discovery in the early 90s [1,2,3], fluctuation theorems have been attracting increasing interest. They establish general features of fluctuating systems away from thermal equilibrium, see Refs. 4, 5 for reviews. A major "test bed" for fluctuation theorems is provided by dynamical systems with a few degrees of freedom coupled to a thermal bath, a Brownian particle being an example. Much of the corresponding theoretical and experimental work refers to (i) modulated linear systems, where fluctuations have been studied both in transient and stationary regimes [6,7,8,9,10,11,12], and (ii) nonlinear systems, initially at thermal equilibrium, driven to a different, generally nonequilibrium state [13,14,15,16,17].Fluctuations in nonequilibrium dynamical systems have been attracting attention also in a different context. They play an important role in various types of mesoscopic vibrational systems of current interest. Because damping of the vibrations is typically weak, even a moderately strong resonant force can excite them to comparatively large amplitudes, where the nonlinearity becomes substantial. As a result, the system may have two or more coexisting stable states of forced vibrations [18]. Fluctuations can cause switching between these states [19] and thus significantly affect the overall behavior of the system even where they are small on average. Many features of the switching behavior and a range of phenomena and applications related to the switching, from quantum measurements to resonant frequency mixing and to high-frequency stochastic resonance have been studied experimentally [20,21,22,23,24,25,26,27,28].In this paper we analyze work fluctuations in periodically modulated nonlinear dynamical systems coupled to a bath. We derive the stationary state work fluctuation theorem and show that, under fairly general assumptions, the distribution of fluctuations of work done by the modulating force over a long time τ is Gaussian. In common with systems close to thermal equilibrium, the work variance σ 2 is proportional to the average work W , but the proportionality coefficient is not universal and depends on system parameters. It becomes exponentially large in bistable systems in the range of a kinetic phase transition where the stationary populations of the vibrational states are close to each other. This parameter range has similarity with the region of a first-order phase transition where molar fractions of the coexisting phases ar...

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A fluctuation theorem for non-equilibrium relaxational systems driven by external forces

Abstract: Note that the "classical" Green-Kubo relation involves the total flux J t = J w t + J H t . For the latter one has, in the adiabatic approximation,

Cited by 121 publications

References 64 publications

Anomalous Fluctuation Relations

Anomalous Fluctuation Relations

Chaotic Hypothesis, Fluctuation Theorem and Singularities

Exponential peak and scaling of work fluctuations in modulated systems

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